Winchester "Stealth" in 308Winchester or a Remington 700 VS or PSS in 308Winchester...
In the case of the Remingtons, if they don't shoot perfect from the factory have the barrel set back and receiver/barrel trued by a competent gunsmith then rechamber. Gun should shoot very well after that.
For scope, if you are an optics snob take your pic of any one of several very nice scopes out there. If not and you want to save a few bucks, I'm actually fairly impressed with Bushnell's 10x Elite 3200 with mil-dot reticle. For around 200 bucks the money saved will allow you to get some nice rings and and something like a 20MOA base for helping shoot to longer ranges.
I've got the Elite 3200 10x on my 300WinMag, bought it only for load development work on my 300WinMag while I wait to rebuild the rifle and buy a more substantial scope. The little Elite 3200 has held up very well and proven to be a very nice little scope for the money. It's goinna be a scope that I keep for other rifles in the future, maybe even get a second one for the AR15 so the rifle can be used as a spotter's rifle along side the 300WinMag.
A pretty nice rifle could be built by using the above combination of rifle and scope while leaving a bit of left over cash for ammo and some gear.
Figure Rem 700 VS in 308, around 650-750 depending on market in your location. The Bushnell Elite 3200 for right around 200. A set of nice rings and a base for between 80-200 dollars depending on how fancy you go. Then a nice bipod, ammo, and a decent shooting mat/case for another 300.